1. Medians, and Altitudes

2. Objectives
Identify and use medians and altitudes in ∆s

3. Medians
A median is a segment whose endpoints are a vertex of a ∆ and the midpoint of the side opposite the vertex. Every ∆ has three medians.
These medians intersect at a common point called the centroid.
The centroid is the point of balance for a ∆.

4. Medians (continued)
Theorem 5.7 (Centroid Theorem) The centroid of a ∆ is located two thirds of the distance from a vertex to the midpoint of the side opposite the vertex on a median.

5. Altitudes
An altitude of a ∆ is a segment from a vertex to the line containing the opposite side and ┴ to the line containing that side. Every ∆ has three altitudes.
The intersection point of the altitudes of a ∆ is called the orthocenter.

6. Altitudes (continued)
Orthocenter

7. Example 1:
ALGEBRA: Points U, V, and W are the midpoints of respectively. Find a, b, and c.

8. Example 1: Find a. Segment Addition Postulate Centroid Theorem
Substitution
Multiply each side by 3 and simplify.
Subtract 14.8 from each side.
Divide each side by 4.

9. Example 1: Find b. Segment Addition Postulate Centroid Theorem
Substitution
Multiply each side by 3 and simplify.
Subtract 6b from each side.
Subtract 6 from each side.
Divide each side by 3.

10. Example 1: Find c. Segment Addition Postulate Centroid Theorem
Substitution
Multiply each side by 3 and simplify.
Subtract 30.4 from each side.
Divide each side by 10.
Answer:

11. Your Turn:
ALGEBRA: Points T, H, and G are the midpoints of respectively. Find w, x, and y.
Answer: